1983 AHSME Problems/Problem 2

Problem

Point $P$ is outside circle $C$ on the plane. At most how many points on $C$ are $3 \ \text{cm}$ from $P$ ?

$\textbf{(A)} \ 1 \qquad \textbf{(B)} \ 2 \qquad \textbf{(C)} \ 3 \qquad \textbf{(D)} \ 4 \qquad \textbf{(E)} \ 8$

Solution

The points $3 \ \text{cm}$ away from $P$ can be represented as a circle centered at $P$ with radius $3 \ \text{cm}$ . The maximum number of intersection points of two circles is $\boxed{(\text{B}) \; 2}$

1983 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1983 AHSME Problems/Problem 2

Problem

Solution

See Also